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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Product spaces in locales
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by John Isbell PDF
Proc. Amer. Math. Soc. 81 (1981), 116-118 Request permission

Abstract:

The embedding of sober spaces in locales preserves products $X \times Y$ where $X$ is quasi-locally compact. A completely regular space $X$ has this preservation property, for all $Y$, if and only if $X$ is a complemented sublocale of a compact space. Equivalently, every closed subset of $X$ is locally compact somewhere.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 81 (1981), 116-118
  • MSC: Primary 54B10
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0589150-5
  • MathSciNet review: 589150